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Usenet Newsgroups : rec.puzzles Hall of Fame

The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

Hall of Fame
Categories : analysis : irrational.stamp.p

You have an ink stamp which is so amazingly precise that, when inked
and pressed down on the plane, it makes every circle of irrational
radius (centered at the center of the stamp) black.

Question:  Can one use the stamp three times and make every point
in the plane black?  [assume plane was white to begin with, and
ignore the fact that no such stamp is physically possible]

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